In a pot, combine beef brisket, water, onion, green onion, and garlic. Cook over medium low heat for about 1.5 hours. Discard the vegetables, keep the stock, and cool the meat from the stock. Shred the meat using a knife or hands and add sesame oil to the meat.

Soak the rice cakes in cold water for 15 minutes. Discard the water after 15 minutes.

Meanwhile, prepare the toppings.

Boil the stock in a clean pot. Add minced garlic, soy sauce, and the rice cakes, and cook for 2-3 minutes. Do not overcook the rice cakes. Adjust the taste by adding salt and add a pinch of black pepper.

Serve the soup in a bowl and add toppings on top.